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AP Statistics Ch. 11: Simulations

#1: Three Children Families

A family doctor is told by a couple that they wish to have three children and that they wonder what the possibility of having all of one sex of a child will be. They think that it will be the same as having 2 girls and 1 boy or having 2 boys and 1 girl. The doctor gives them an assignment to simulate having three children to answer their question. He recommends they count the number of girls out of the 3 children.

1. Write instructions for conducting simulations using the whole table below.

Identify events & their probabilities:

State random generator & assign numbers to events:

One trial =

Response Variable =

Total # of trials =

2. Perform the trials and record the results:

39634 62349 74088 65564 16379 19713 39153 69459 17986 24537 14595

35050 40469 27478 44526 67331 93365 54526 22356 93208 02746 20469

|Type of Family (# girls) |Frequency (#) Rel. Freq (%) |

|No girls (X = 0) | |

|One girl and two boys (X = 1) | |

|Two girls and one boy (X = 2) | |

|Three girls (X = 3) | |

|Total Number of Trials | |

3. What is the probability of having all of one sex? (3 girls or 3 boys)

4. What is the probability of having less than 2 girls?

5. What is the average number of girls?

#2: Having a Boy

Another family has met with the family doctor. They desperately want a boy and are willing to have as many children as possible until they get a son.

1. Write instructions for conducting simulations using the entire first line of the table below.

Identify events & their probabilities:

State random generator & assign numbers to events:

One trial =

Response Variable =

Total # of trials =

2. Perform the trials and record the results (just use the first line of the table):

39634 62349 74088 65564 16379 19713 39153 69459 17986 24537 14595 35050 40469 27478 44526

67331 93365 54526 22356 93208 30734 71571 83722 79712 25775 65178 07763 82928 31131 30196

64628 89126 91254 24090 25752 03091 39411 73146 06089 15630 42831 95113 43511 42082 15140

34733 68076 18292 69486 80468 80583 70361 41047 26792 78466 03395 17635 09697 82447 31405

|Number of Children |Frequency (#) |Relative Frequency (%) |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

3. What is the average number of children they will have before they get a boy?

4. What is the probability they have 2 children or less?

5. What is the probability they have more than 3 children?

#3: Football

A quarterback completes 65% of his passes. Suppose he attempts 12 passes in a game. We are interested in the number of completions each game.

1. Write instructions for conducting 6 simulation trials that show the results for each of the twelve passes in a game.

Identify events & their probabilities:

State random generator & assign numbers to events:

One trial =

Response Variable =

Total # of trials =

2. Conduct 6 trials using the following table of random digits. Be sure to label your results.

80583 70361 41047 26792 78466 03395 17635 09697 82447 31405 00209 90404

99457 72570 42194 49043 24330 14939 09865 45906 30734 71571 83722 79712

25775 65178 07763 82928 31131 30196 02740 03750 07304 96621 10472 03745

3. Based on your simulation what is the mean number of passes he will make in a game?

#4: A receiver on the same team catches the ball 78% of the time. The coach has told him he will stay in the game unless he drops a pass- then he will be benched for the rest of the game. He usually has 9 passes thrown to him in a game.

1. Write instructions for conducting 10 simulation trials, looking at the number of passes caught per game.

2. Conduct 10 trials using the following table of random digits. Be sure to label/record your results.

05409 20830 01911 60767 55248 79253 12317 84120 77772 50103 95836 22530

91785 80210 34361 52228 33869 94332 83868 61672 92749 09287 02756 01846

3. Based on your simulation what is the chance he will get benched in a game?

#5: Simulating getting Prizes from a Cereal Box

Your favorite cereal is giving out Simpson toys as a promotion. One of six toys will be placed randomly in a cereal box. Assuming that shipment of the boxes is random also how many boxes would you have to buy to get all six toys?

1. Write instructions for conducting one simulation trial.

2. With a partner run 10 trials of this simulation and record the results.

95836 22530 91785 80210 34361 52228 33869 94332 83868 61672 65358 70469 87149 89509

72176 18103 55169 79954 72002 20582 72249 04037 36192 40221 14918 53437 60571 40995

55006 10694 41692 40581 93050 48734 34652 41577 04631 49184 39295 81776 61885 50796

96822 82002 07973 52925 75467 86013 98072 91942 48917 48129 48624 48248 91465 54898

61220 18721 67387 66575 88378 84299 12193 03785 49314 39761 99132 28775 45276 91816

|Number of Boxes Purchased |Frequency |

|6 | |

|7 | |

|8 | |

|9 | |

|10 | |

|11 | |

|12 | |

|13 | |

|14 | |

|15 | |

|16+ | |

3. What is the average number of boxes needed to get all six toys?

4. What is the probability that it would take more than 12 boxes to get all six toys?

5. What is the probability that it would take less than 10 boxes?

6. What is the probability that it would take between 8 and 12 boxes to get all six toys?

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